Add and Subtract Square Roots

Adding and subtracting like radicals. In MathBound, the free Algebra I adventure game, Carrot Bundler asks these problems, and the only way past is to solve them.

Part of Radicals and More Functions: chapter 11 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Add/Subtract Like Radicals. Add or subtract square roots with identical radicands by combining their coefficients.
Simplify Before Adding/Subtracting. Simplify one square root so its radicand matches another term before combining.
Variables in Radicands. Simplify and combine square roots containing a single variable with an odd exponent.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Add/Subtract Like Radicals

Simplify:

72 + 52 - 22

$106$
$10$
$142$
$102$

Show the worked steps

$The$ $radicands$ $match,$ $so$ $combine$ $the$ $coefficients$ $only.$
$7 + 5 - 2 = 10 .$

Answer: $102$

Example 2 · Simplify Before Adding/Subtracting

Which

radical

can

be

combined

with

2 ?

$8$
$4$
$9$
$44$

Show the worked steps

$Simplify$ $each$ $one$ $and$ $look$ $for$ $2$ $left$ $over.$
$8 = 22,$ $a$ $like$ $radical.$

Answer: $8$

Example 3 · Variables in Radicands

Simplify:

28 x^{3} - x 7 x

$x 7 x$
$x^{2} 7 x$
$2 x 7 x$
$3 x 7 x$

Show the worked steps

$28 x^{3} = 2 x 7 x .$
$Subtracting$ $x 7 x$ $leaves$ $x 7 x .$

Answer: $x 7 x$

Where it is in your textbook

Textbook	Lessons
Standard course	11.1
Big Ideas Math Algebra 1	9.1
Big Ideas Math Algebra 1 (2022)	9.1
Glencoe Algebra 1	10-3
Math Nation Algebra 1 (Florida B.E.S.T.)	1.9
OpenStax Elementary Algebra 2e	9.3
Pearson Algebra 1 Common Core	10-3
Reveal Algebra 1	8-6
SpringBoard Algebra 1	20

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